We make inference for a competing risks model under the assumption that observations are left-truncated and right-censored and failure causes are partially observed. When the latent failure times follow a generalized family of distributions, inference for unknown parameters is provided using classical and Bayesian approaches. Particularly existence-uniqueness properties of maximum likelihood estimators are established. Subsequently interval estimators are constructed based on observed Fisher information matrix. Bayes estimates and associated highest posterior density intervals are developed using gamma-beta prior distributions by considering squared error loss function. We also study estimation problem when parameters are order restricted. The performance of all estimators is evaluated based on an extensive simulation study and comments are obtained. A real data set is also analyzed for illustration purposes.